WASHINGTON (AP) — The House is set to go along with a bipartisan Senate compromise that would link college students’ interest rates to the financial markets and offer borrowers lower rates this fall.

The Senate bill hews closely to one the House already has passed, and leaders from both parties and in both chambers expect those differences won’t stand in the way of quick resolution, perhaps as early as Wednesday.

House approval would send the measure to President Barack Obama, who has said he would sign it into law “right away.”

But critics note that if the economy improves, as expected, rates could climb higher.

If the Republican-led House consents to the Senate’s tinkering with the House’s earlier proposal, and Obama signs the legislation before students start returning to campus, families would see better deals on some federal loans this year than they did in 2012. Undergraduates could borrow at rates as low as 3.4 percent for subsidized Stafford loans and 6.8 percent on unsubsidized Stafford loans last year, while graduate students and parents borrowed at 7.9 percent last year.

Those 3.4 percent rates doubled on July 1 because Congress did not act. Lawmakers from both parties said the rate increase was unacceptable and worked on various proposals to extend rates, overhaul rates and even remake the entire program before classes start this fall.

Both chambers would link the interest rate to the 10-year Treasury note plus an added percentage, based on the type of loan. Each sets caps on how high the loans can go.

But under the Senate bill, once a student or parent takes a loan for the school year the rate would not change. The House bill would make the interest rate variable, meaning it could change every year until the loan is repaid.

A look at what the House and Senate bills would mean for students and their parents:

UNDERGRADUATES:

Senate: Undergraduates who take subsidized and unsubsidized Stafford loans would pay the 10-year Treasury note, plus an additional 2.05 percent. That would put the interest rate at about 3.9 percent this fall. Rates would be capped at 8.25 percent.

House: Under the House bill, undergraduates who take subsidized and unsubsidized Stafford loans would pay the 10-year Treasury note, plus an additional 2.5 percent. That would translate to an interest rate of about 4.3 percent interest rates for loans taken this fall. Rates would be capped at 8.5 percent.

GRADUATE STUDENTS:

Senate: Graduate students would borrow at the interest rate of the 10-year Treasury notes plus an additional 3.6 percent. That would bring 5.4 percent interest rates for borrowers this fall. Rates would be capped at 9.5 percent.

House: Graduate students and parents would borrow at the 10-year Treasury note plus an additional 4.5 percent. Under this formula, graduate student loans this fall would carry a 6.3 percent interest rate. Rates would be capped at 10.5 percent.

PARENTS AND SOME GRADUATE STUDENTS:

Senate: Parents and some graduate students would borrow at the 10-year Treasury note plus an additional 4.6 percent. That works out to a 6.4 percent interest rate for fall term. Rates would be capped at 10.5 percent.

House: Graduate students and parents would borrow at the 10-year Treasury note plus an additional 4.5 percent. That would bring about 6.3 percent interest rates for borrowers this fall. Rates would be capped at 10.5 percent